Journal ofMaterials Chemistry A

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Thermoelectric p

aState Key Laboratory of New Ceramics a

Science and Engineering, Tsinghua Univ

jingfeng@mail.tsinghua.edu.cn; Fax: +86-62bMaterials Science, California Institute of Te

† Electronic supplementary informationand calculation of the Lorenz number. Se

‡ Tian-Ran Wei and Heng Wang contribu

Cite this: J. Mater. Chem. A, 2014, 2,13527

Received 20th April 2014Accepted 16th June 2014

DOI: 10.1039/c4ta01957a

www.rsc.org/MaterialsA

This journal is © The Royal Society of C

roperties of Sn-doped p-typeCu3SbSe4: a compound with large effective massand small band gap†

Tian-Ran Wei,‡a Heng Wang,‡b Zachary M. Gibbs,b Chao-Feng Wu,a

G. Jeffrey Snyderb and Jing-Feng Li*a

Cu3SbSe4-based compounds composed of earth-abundant elements have been found to exhibit good

thermoelectric performance at medium temperatures. High zT values were achieved in previous studies,

but further insight into the transport mechanism as well as some key material parameters is still needed. In

this work, we studied the electrical and thermal transport properties of Sn-doped Cu3SbSe4 between 300 K

and 673 K. It was found that the single parabolic band model explains the electrical transport very well.

Experimentally, we determined the band gap to be around 0.29 eV. The density-of-state effective mass

was found to be about 1.5 me for the doped samples. The transport properties suggested degeneracy

splitting near the valence band maximum that was not captured by previous band structure calculations.

The maximum zT � 0.70 was obtained at 673 K, and the optimized carrier density was �1.8 � 1020 cm�3,

and the potential for further improvement of zT via material engineering is briefly discussed.

Introduction

Thermoelectric materials, which can realize the direct conver-sion between heat and electricity in the solid state, are expectedto play a signicant role in the eld of clean energy developmentand utilization.1 Developing materials with a high gure ofmerit, zT, dened as zT ¼ S2T/rk (S, T, r and k are the Seebeckcoefficient, absolute temperature, electrical resistivity andthermal conductivity, respectively), has been the main topic ofresearch in thermoelectrics.2–6 Recently, copper chalcogenideshave received increasing attention as promising thermoelectricmaterials with a high zT, such as superionic Cu2Se7�9 withliquid-like phonon behaviour and layered oxyselenide BiCu-SeO.10–13 Other high-symmetry ternary or multinary copperchalcogenides composed of Cu–M (M is a chalcogen) tetrahe-dral bonds include chalcopyrite, tetrahedrite and famatinite,etc. Many of these compounds have also been found to bepromising thermoelectrics, such as CuGaTe2,14,15 CuInTe2,16

Cu2.1Zn0.9SnSe4,17 Cu2ZnGeSe418 and Cu3SbM4 (M ¼ Se, S),19,20

even Cu12Sb4S13 and Cu12As4S13 right from their naturalmineral form.21,22 Among these compounds, Cu3SbSe4 is a p-type semiconductor with a small band gap. Previous

nd Fine Processing, School of Materials

ersity, Beijing 100084, China. E-mail:

771160; Tel: +86-10-62784845

chnology, Pasadena, CA 91125, USA

(ESI) available: Enlarged XRD patternse DOI: 10.1039/c4ta01957a

ted equally to this work.

hemistry 2014

investigations have been carried out focusing on adjusting thecarrier density and forming solid solutions towards high zT.23,24

In spite of the knowledge that has already been obtained forCu3SbSe4, the insight into the transport mechanism as well assome key material parameters that are essential for furtheroptimization towards higher zT is still inadequate. In this work,we take a close look at the transport properties of p-typeCu3SbSe4. Our samples were prepared by mechanical alloyingand spark plasma sintering. This simple method led to highquality samples with a homogeneous microstructure, nearlyideal doping efficiency and well behaved transport properties.This compound was found to be a semiconductor with a largeeffective mass of about 1.5 me (when doped) and a small bandgap of �0.29 eV. The transport data also suggest a split ofvalence bands that was not revealed by previous calculations.These ndings provide an in-depth understanding of thepromising zT and the possible strategies for further materialengineering.

Experimental

Samples with nominal compositions of Cu2.95Sb1�xSnxSe4 (x ¼0, 0.01, 0.02, 0.03, 0.04) were fabricated via mechanical alloying(MA) and spark plasma sintering (SPS). A Cu deciency ischosen to compensate for Se volatilization and achieve the bestperformance, which was discussed in detail in a previousreport.25 A mixture of Cu, Sb, Sn and Se powders of high puritywere milled in a stainless steel vessel on a planetary ball mill at425 rpm for 10 hours protected by a mixed atmosphere of95 vol% Ar and 5 vol% H2 gases and were then milled in an

J. Mater. Chem. A, 2014, 2, 13527–13533 | 13527

Fig. 1 XRD patterns of Cu2.95Sb1�xSnxSe4. No peak shift due to Sndoping can be seen.

Fig. 2 Morphology and elemental distribution of bulkCu2.95Sb0.98Sn0.02Se4: (a) SE2 image of a fractured surface; (b) SE2image, (c) BSE image and (d) EPMA mapping of main elements ofpolished surface.

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alcohol solution. The as-synthesized powders were sintered bySPS at 703 K for 5 min under a uniaxial pressure of 50 MPa intodisk-shaped samples about 3 mm in thickness and about 93%or higher in relative density.

The phase structures were investigated by X-ray diffraction(XRD) with a D/max-RB diffractometer (Rigaku, Japan) using CuKa radiation. Scanning electron microscopy (SEM) images ofthe bulk materials were taken in the secondary electron detector(SE2) mode and the backscattering electron (BSE) mode by eldemission scanning electron microscopy (FE-SEM, JSM-7001,JEOL, Japan). Electronic probe microscopic analysis (EPMA,JXA-8230, JEOL, Japan) was used to analyze the ratio anddistribution of the elements on polished surface of bulksamples. Bar-shaped specimens were cut along the radialdirection of a disk sample for measurements of the Seebeckcoefficient (S) and the electrical resistivity (r) as a function oftemperature using a Seebeck coefficient/electric resistancemeasuring system (ZEM-2, Ulvac-Riko, Japan). The Hall coeffi-cient (RH) at and above 300 K was measured under a reversiblemagnetic eld by the van der Pauw technique using a Hallmeasurement system (8340DC, Toyo, Japan). The Hall carrierdensity (nH) was calculated via nH ¼ 1/(eRH), and the Hall carriermobility (mH) was obtained using the relationship, mH ¼ RH/r.The thermal diffusivity (D) was measured in the thicknessdirection of a disk-shaped sample of f 10 mm and about 1.5mm in thickness using a laser ash diffusivity method (TC9000,Ulvac-Riko, Japan). The specic heat capacity (CP) wasmeasured using the Quantum Design physical propertymeasurement system (PPMS) as well as the Netsch LFA 457 laserash thermoanalysis system. The thermal conductivity (k) wascalculated by k ¼ DCpd, where d is the density measured by theArchimedes method. Optical absorption edge measurementswere carried out on the undoped sample using a Nicolet 6700FTIR Spectrophotometer equipped with a Praying MantisDiffuse Reectance attachment (Harrick Scientic Instruments)at room temperature and up to 573 K. The scans were refer-enced to KBr standard samples. The optical gaps were obtainedby extrapolating a, the absorption coefficient, to 0 as a functionof (hn)n, where hn is the photon energy, and n is equal to 2 fordirect gaps, 0.5 for indirect gaps.

Results and discussion

The XRD patterns of the samples subjected to SPS are shown inFig. 1, which suggest single phase Cu3SbSe4 (PDF #85-0003)regardless of the Sn content. No peak shi even at high angleswas found with the doping of Sn due to the small difference inionic size26 between Sn4+ and Sb5+ and the low doping level. Themorphology of the fractured and polished surfaces of a repre-sentative sample of Cu2.95Sb0.98Sn0.02Se4 is shown in Fig. 2. Thefractured surface exhibits well crystallized grains with anaverage grain size of �2 mm. The back scattering electron (BSE)graph and EPMA mapping conrmed a homogeneous distri-bution of elements without the segregation of secondaryphases.

Undoped Cu3SbSe4 is an intrinsic semiconductor with acarrier density in the order of 1018 cm�3. Substituting Sn for Sb

13528 | J. Mater. Chem. A, 2014, 2, 13527–13533

continuously increases the carrier density up to 2 � 1020 cm�3.There has been debate on the specic valence number of Sb inCu3SbSe4, both 5+ and 3 + have been suggested.27–29 Nonethe-less, with a simple argument that Sn has one less valenceelectron than Sb and is tetrahedrally bonded just as Sb in thestructure, each Sn is expected to donate one free hole. Thistrend is well followed for the samples in the present study, asshown in Fig. 3: the measured Hall carrier density nH at roomtemperature follows exactly the calculated result (solid line)based on the density of substitutional Sn atoms assuming eachof them contribute one free hole, using the single parabolicband (SPB) model (which determines the Hall factor rH thatlinks nH with the chemical carrier density n via nH ¼ n/rH).

Fig. 4 shows the electrical resistivity (r) and Seebeck coeffi-cient (S) as functions of temperature. All the samples showed p-type character. The undoped sample exhibited a nondegenerate

This journal is © The Royal Society of Chemistry 2014

Fig. 3 Hall carrier density as a function of the dopant density at roomtemperature. The solid line was calculated by SPB assuming each Sndonates one free hole.

Fig. 4 (a) Electrical resistivity and (b) Seebeck coefficient as functionsof temperature.

Fig. 5 Band gap by optical absorption edge measurements in undo-

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behaviour with a relatively large and decreasing Seebeck coef-cient and resistivity with increasing temperature. From S ofthe undoped sample, the band gap Eg was estimated to be about0.29 eV via30

Eg ¼ 2eSmaxTSmax. (1)

This estimate is consistent with the band gap measured bythe optical absorption spectrum, which indicates a clear direct

This journal is © The Royal Society of Chemistry 2014

transition at 0.29 eV, as shown in Fig. 5. Previously, a similarband gap was reported by Berger et al. using the opticalmethod.31 We have also noticed that a much smaller gap of0.13 eV was suggested by Nakanishi et al. by analyzing thetemperature dependence of electrical resistivity and Hall coef-cient, and 0.11 eV via the infrared transmission spectra.32 Asimilar value was also obtained by Li et al. by tting the elec-trical resistivity against temperature.33 In fact, we found asimilar activation energy of DE � 0.13 eV in this study by ttingthe linear relation, ln r�1/T, from the undoped sample.Further, our optical absorption measurements showed a veryweak absorption above 0.12 eV, possibly corresponding to anindirect transition. However, we conclude that the activationenergy of 0.12 eV is unlikely to be the primary band gap, becausethe large S values in undoped samples would not be achievable.In order to maintain a high Seebeck coefficient (�400 mV K�1 at�300 K), the chemical potential needs to be deep in the gap,while a small gap of 0.12 eV would inevitably induce signicantminority carriers that compensate for the Seebeck value. As aresult, the band gap is believed to be 0.29 eV corresponding to adirect transition, which is several orders of magnitude strongerthan the supposed indirect transition. The activation energy of0.12 eV is then speculated to be due to defect levels inside theband gap. Nakanishi et al. were not able to observe the muchstronger direct transition because they used the optical trans-mission, which had already been saturated to zero throughputaer the rst indirect transition at 0.12 eV. A band gap around0.3 eV is comparable with other good thermoelectrics, such asPbTe34–36 or PbSe,37–39 Mg2Si0.4Sn0.6 (ref. 40) and ZrNiSn.41 Inaddition, small band gaps usually mean less ionic character,making it easier for delocalized charge carriers that lead to highmobilities desirable for thermoelectrics. However, the disad-vantage of a small band gap is the tendency of the excitation ofminority carriers.

The measured Hall mobility, mH, of all samples decreasedwith increasing temperature [Fig. 6(a)]. Near room temperature,the T�3/2 law is roughly obeyed by all samples, indicating thedominance of acoustic phonon scattering of carriers. Fig. 6(b)shows the measured nH at different temperatures. For eachdoped sample, nH remains constant near room temperature and

ped Cu3SbSe4.

J. Mater. Chem. A, 2014, 2, 13527–13533 | 13529

Fig. 6 (a) Hall mobility and (b) Hall carrier density as functions oftemperature for Cu2.95Sb1�xSnxSe4. The Hall carrier density of theundoped sample is depicted in the inset of (b).

Fig. 7 Change in (a) Seebeck coefficient and (b) Hall mobility with theHall carrier density at room temperature. The inset in (a) shows theeffective mass for each sample determined from S and nH.

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above 500 K, it slowly increases with temperature. Considering asmall and temperature-independent Eg ¼ 0.29 eV in Cu3SbSe4,the apparent increase in nH is likely due to bipolar excitation.

Fig. 7 shows the carrier density dependence of the Seebeckcoefficient and Hall mobility at room temperature, togetherwith the data previously reported for this system.23,33,42 Wefound that the SPB model with acoustic phonon scatteringassumption could well explain both properties. From the carrierdensity dependence of the Seebeck coefficient (the Pisarenkorelation), it seems that all the measured S are consistent with aconstant density-of-state (DOS) effective mass, m* ¼ 1.5 me.However, a range of m* values from 1.1 me to 1.7 me areacceptable. In fact, by calculating m* for each individualsample, we found a clear increase when going from undoped todoped samples [inset of Fig. 7(a), error bars are estimatedassuming 5% uncertainty in S measurement that is normallyseen]. A large effective mass usually means less mobile carriersand a lower thermoelectric quality factor dened as:

B ¼ 2kB2ħ

3p

dvl2NV

m*IX

2kLT (2)

where vl is the longitudinal speed of sound, d is the density, NV

is the degeneracy of band,mI* is the inertial effective mass, kL isthe lattice thermal conductivity, and X is the deformationpotential coefficient.43 However, in the case of Cu3SbSe4, thelarge m* comes from three bands that are degenerate (sug-gested by calculation29) at the valence band maximum. As

13530 | J. Mater. Chem. A, 2014, 2, 13527–13533

known in lead chalcogenides, a large effective mass from highlydegenerate bands is favourable for high thermoelectricperformance.35

The changing m* with doping level is also indicated by thecarrier density dependence of the Hall mobility mH. In the SPBmodel, mH of a system with a reduced chemical potential h canbe expressed as:43

mH ¼ 3ffiffiffiffip

p8

m0

F�1=2ðhÞF0ðhÞ ¼ peħ4dvl2NV

5=3

2ffiffiffi2

pm*5=2ðkBTÞ3=2X2

F�1=2ðhÞF0ðhÞ (3)

FnðhÞ ¼ðN0

xndx

1þ expðx� hÞ (4)

where m0 is the nondegenerate limit of mobility governed by theacoustic phonon scattering process. We found that for dopedsamples, the SPB model provides a good t with m0 determinedto be 49 cm2 V�1 s�1. The measured mobility of the undopedsample on the other hand, is about twice as high as this value.We notice that all available reports23,33,42 on undoped samplesagree with our ndings. Furthermore, for the sample studied inthis work, this result is repeatable in at least two measurementsfrom room temperature to 673 K. So the high mobilities areunlikely to be due to measurement error or non-equilibriumconditions. Using the SPB model, the difference can be wellexplained by the variation in effective mass considering m* is1.1 me for the undoped sample and 1.5 me for doped ones, assuggested in the inset of Fig. 7(a).

This journal is © The Royal Society of Chemistry 2014

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Previous band structure calculations for Cu3SbSe4 suggesteda maximum of the valence band at the G point where threebands with different effective masses are degenerate.29 Theobserved Pisarenko relation at 300 K, however, clearly implies achanging effective mass that cannot be explained by multipledegenerate bands. The observed transport properties insteadsuggest a split of at least two of these three bands near themaximum, possibly due to spin-orbit coupling, which was notconsidered in the reported calculation. Consequently, as thechemical potential moves deep into the valence bands withincreasing carrier density, the secondary bands begin to play amore noticeable role in transport, leading to a larger m* whenthe system is characterized with the SPB model.

While the observed Pisarenko relation and changing effec-tive mass with increased doping level can be simply explainedby the split of bands near the valence band maximum, thecarrier density dependence of the mobility [seen in Fig. 7(b)]requires more complicated physics to completely understand it.Even with the band conguration, one would not expect thetrend in Fig. 7(b) without allowing for inter-band scattering oradditional scattering mechanisms associated with theincreased density of dopants. Nonetheless, for the dopedsamples, which are of most interest to thermoelectrics, the SPBmodel with acoustic phonon scattering assumption stillprovides an effective way to understand the transport proper-ties. With the reported vl of 3643 m s�1,27 and assuming NV ¼3,29 the deformation potential coefficient X, was found to be15 � 0.5 eV at 300 K. This value is smaller than those found insystems with a smaller effective mass, such as lead chalcogen-ides44,45 and Bi2Te3,46 whereas it is noticeably larger whencompared with systems with a larger effective mass (>1 me for asingle valley), such as La3Te4 (ref. 47), Yb14MnSb11 (ref. 48) andZrNiSn.49

To determine the thermal conductivity of the samples, Cp

was measured between 300 K and 673 K, and the values areshown in Fig. 8. We notice that the measured results from twodifferent instruments, while consistent with each other, areconsiderably higher than the Dulong–Petit CV. Above the Debyetemperature (131 K by Berger et al.,31 60–80 K by Zhang et al.27

Fig. 8 Heat capacity as a function of temperature for undopedCu3SbSe4. Skoug's result is 1.85 J cm�3 K�1 in ref. 20 and was con-verted to 0.36 J g�1 K�1 by assuming the relative density to be 90%.

This journal is © The Royal Society of Chemistry 2014

and 65 K by Skoug et al.50), the CP for solids is generally largerthan CV due to lattice expansion. While this qualitativelyexplains the linear increase in CP with temperature, the differ-ence at room temperature (20%) is much larger than one wouldexpect. The difficulty in an accurate determination of CP

experimentally and thus the different values used by differentstudies is partially responsible for the difference in the reportedzT values.

Fig. 9 shows the total thermal conductivity and the latticethermal conductivity as functions of temperature. The electronicthermal conductivity ke was calculated by ke ¼ LT/r, where theLorenz number L, was calculated with the SPB model. The latticethermal conductivity kL decreased with temperature followingT�1 (dashed line), which indicates the dominance of phonon–phonon Umklapp scattering in phonon transport. Even in theundoped sample, kL decreased with T over the whole measure-ment range, and no obvious bipolar contribution was observed.Owing to the low percentage of Sn substitution and the small sizedifference between Sb and Sn, no difference in kL between dopedand undoped samples was observed. The minimum latticethermal conductivity for Cu3SbSe4, kmin, was estimated usingCahill's formula51 and was found be around 0.47 Wm�1 K�1

from 275 K to 700 K. Experimentally, kL at 673 K was around1.1 Wm�1 K�1, so a further reduction of kL is possible.

The gure of merit, zT, is shown as a function of temperaturein Fig. 10(a). The maximum value�0.70 was reached at 673 K inthe sample with 2% Sn doping, and the corresponding Hallcarrier density was �1.8 � 1020 cm�3. We further calculated zT

Fig. 9 (a) Total thermal conductivity and (b) lattice thermal conduc-tivity as functions of temperature.

J. Mater. Chem. A, 2014, 2, 13527–13533 | 13531

Fig. 10 zT as a function of (a) temperature and (b) Hall carrier densityfor Sn-doped Cu3SbSe4. Solid curves were calculated with SPB modelusing the parameters for doped samples determined at 300 K.

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as a function of nH from the SPBmodel using the parameters fordoped samples determined at 300 K. The result is shown inFig. 10(b). The optimal carrier density corresponding to thehighest zT increased from�4–5 � 1019 cm�3 at 300 K to �1–2�1020 cm�3 at 673 K, as demonstrated experimentally and theo-retically. According to the modeling, zT signicantly higherthan 0.7 is unlikely for Cu3SbSe4 just by tuning the carrierdensity. Two possible routes to a higher zT via material engi-neering are: rst by tuning the position of individual valencebands, so they are better aligned at the maximum, and secondby forming solid solutions which reduce kL. It should be notedthat at high temperatures, Cu3SbSe4 has an inherent kL onlytwice as high as the theoretical minimum (comparable to thecase of PbTe or PbSe where kL is around 0.7 Wm�1 K�1 and kmin

is around 0.4 Wm�1 K�1) and that forming a solid solution willalso decrease the carrier mobility. Therefore, forming solidsolutions would likely increase zT but not signicantly. Actuallythe zT value reported for Cu3SbSe4�xSx is 0.89: about a 20%increase over that of Cu3SbSe4 reported by the same group.20,23

Conclusions

Polycrystalline Cu3SbSe4 doped with Sn were fabricated withhigh phase purity and a precisely controlled carrier density bymechanical alloying and spark plasma sintering. The transportbehaviour of this compound was explained by the single

13532 | J. Mater. Chem. A, 2014, 2, 13527–13533

parabolic band (SPB) model. The Seebeck coefficients andmobilities at 300 K of the samples with different doping levelssuggested a split of the bands at the valence band maximum,which according to previous calculations are triply degenerate.The transport data and optical band gap measurements sug-gested a direct band gap of �0.29 eV, which is temperatureindependent. The thermal conductivity was governed byUmklapp phonon scattering, and a T�1 dependence wasobserved for all samples. The maximum zT value of �0.70 wasobtained at 673 K with 2% Sn (Hall carrier density 1.8 �1020 cm�3). The analyses and ndings in this study wouldpotentially help the understanding of transport properties insimilar Cu-based ternary or multinary thermoelectric materials.

Acknowledgements

This work was supported by National Natural Science Founda-tion (no. 51172121) and the National Basic Research Program ofChina (Grant no. 2013CB632503) as well as 863 Program underGrant no. 2012AA051104. H. W., Z. M. G and G. J. S. acknowl-edge the support from the AFOSR MURI program in USA andthe Molecular Materials Research Center (MMRC) at Caltech foroptical measurement instruments.

Notes and references

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